Method of producing matched coating composition and device used therefor

ABSTRACT

The present invention is directed to a method and device that use spectral measurements of the color of a target coating on a substrate, such as auto body being matched. The method utilizes pigment mixture models to produce a matched coating composition that when applied as a coating matches in appearance with that of the target coating, while also providing other desired coating properties, such as durability, gloss and adhesion. The method of the present invention is well suited for producing automotive refinish paints used in automotive refinish applications wherein the undamaged portion of the autobody is color matched to produce a matched refinish paint that can be then applied over a repaired portion of autobody.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. Provisional application Ser.No. 60/468,595 filed on May 7, 2003, which is incorporated herein byreference.

FIELD OF INVENTION

The present invention generally relates to a method of producing coatingcompositions that are color matched to target coatings and to a deviceused therein. The method is specially suited for producing color matchedcoating compositions suitable for use in the automotive refinishapplications.

BACKGROUND OF THE INVENTION

In many industries, particularly in the automotive refinish industry,customers demand not only special color effects and good color match,but also exceptionally good appearance and durability. In refinishingcars in the field, portable colorimeters are commonly used to measurethe target color readings off the coating on a car body being repaired,followed by searching through stored databases of paint formulas to findan existing formula that is the closest match with the color readingsmeasured off the car body. Such a process allows a body shop to directlyfind the best paint formula to match the car being repaired. However,these current processes require creation and maintenance of an extensivedatabase containing thousands of refinish car colors from which one canafter exhaustive search select a color match that is closest to thetarget coating. Moreover, the aforedescribed selection process isexpensive since the refinisher has to make and test several paintsamples before a close match to the target coating can be achieved. Thepresent invention helps in producing the closest color matches in acost-effective manner without the need for creating and maintaining anextensive color database.

A method of characterizing a color coating on a surface, such as an autobody, has been disclosed in U.S. Pat. No. 5,231,472. The method utilizedmeasures the reflectance of a reflected light attenuated by the presenceof metal flakes typically used in metallic paints. Several solutions toradiative transfer equations of S. Chandrasekhar correlate theattenuated measured reflectances from a target metallic coating withthose predicted by the solutions to produce a close color match for thetarget metallic coating.

STATEMENT OF THE INVENTION

The present invention is directed to a method for producing a matchedcoating composition for a specified end-use, said method comprising:

(i) measuring reflectances of a target portion of a target coating at aset of preset wavelengths with a spectrophotometer of a coatingcharacterizing device to plot a target spectral curve of said targetportion;

(ii) calculating target color (L,a,b or L,C,h) values of said targetportion from said target spectral curve of said target portion;

(iii) selecting one or more preliminary colorant combinations from astored list of known colorants in accordance with a combinatorialselection criteria to match with said target color values;

(iv) determining concentration of each said known colorant in each ofsaid preliminary colorant combinations in accordance with color matchingcriteria wherein said concentration of each said known colorant isoptimized for optimal match of color values of each of said preliminarycolorant combinations with said target color values;

(v) balancing said preliminary colorant combinations to allow for thepresence of non-colorant components in said matched coating compositionto generate one or more viable combinations optimized in accordance withmixing and regulatory criteria developed for said specified end-use; and

(vi) selecting an optimal viable combination from said viablecombinations in accordance with an acceptability equation for saidspecified end-use, said optimal viable combination having an optimalacceptability value for said specified end-use wherein said knowncolorants and non-colorant components when mixed in accordance with saidoptimal viable combination produce said matched coating composition thatwhen applied as a matched coating visually matches with the appearanceof said target coating.

The present invention is further directed to a color characterizingdevice for producing a matched coating composition for a specifiedend-use, said device comprising:

(i) a spectrophotometer of said device having a base for positioningsaid spectrophotometer over a target portion of a target coating;

(ii) means for calculating target color (L,a,b or L,C,h) values of saidtarget portion;

(iii) a computer usable storage medium located in a computer of saiddevice having computer readable program code means residing therein,said computer readable program code means comprising:

(a) means for configuring computer readable program code devices tocause said computer to select one or more preliminary colorantcombinations from a stored list of known colorants in accordance with acombinatorial selection criteria to match with said target color spacevalues;

(b) means for configuring computer readable program code devices tocause said computer to determine concentration of each said knowncolorant in each of said preliminary colorant combinations in accordancewith color matching criteria wherein said concentration of each saidknown colorant is optimized for optimal match of color values of each ofsaid preliminary colorant combinations with said target color values;

(d) means for configuring computer readable program code devices tocause said computer to balance said preliminary colorant combinations toallow for the presence of non-colorant components in said matchedcoating composition to generate one or more viable combinationsoptimized in accordance with mixing and regulatory criteria developedfor said specified end-use; and

(e) means for configuring computer readable program code devices tocause said computer to select an optimal viable combination from saidviable combinations in accordance with an acceptability equation forsaid specified end-use, said optimal viable combination having anoptimal acceptability value for said specified end-use wherein saidknown colorants and non-colorant components when mixed in accordancewith said optimal viable combination produce said matched coatingcomposition that when applied as a matched coating visually matches withthe appearance of said target coating.

The present invention is still further directed to a method forproducing a matched resin for a specified end-use, said methodcomprising:

(i) measuring reflectances of a target portion of a target substrate ata set of preset wavelengths with a spectrophotometer of a coatingcharacterizing device to plot a target spectral curve of said targetportion; (step by user)

(ii) calculating target color (L,a,b or L,C,h) values of said targetportion from said target spectral curve of said target portion; (part ofstep to done by user)

(iii) selecting one or more preliminary colorant combinations from astored list of known colorants in accordance with a combinatorialselection criteria to match with said target color values; (indevice/computer)

(iv) determining concentrations of each said known colorant in each ofsaid preliminary colorant combinations in accordance with color matchingcriteria to generate one or more intermediate colorant. combinations ofsaid known colorants wherein each of said intermediate colorantcombinations is optimized for optimal color match with said target colorvalues;

(v) balancing said intermediate colorant combinations to allow for thepresence of non-colorant components in said matched coating compositionto generate one or more viable combinations of said known colorants,wherein each of said viable combinations is optimized in accordance withmixing and regulatory practices developed for said specified end-use;and

(vi) selecting an optimal viable combination from said viablecombinations in accordance with an acceptability equation for saidspecified end-use, said optimal viable combination having an optimalacceptability value for said specified end-use wherein components insaid optimal viable combination when mixed produce said matched resinthat when formed as a matched substrate visually matches the appearanceof said target substrate.

BRIEF DESCRIPTION OF DRAWING

FIG. 1 Is a schematic representation of the various components of acolor characterizing device of the present invention.

FIG. 2 shows the comparison of the theoretical spectral curves (linewith data points) that would result by using the matched coatingcomposition containing the preliminary colorant combinations of Formula1 with the measured spectral curve from the target portion of the targetcoating (solid smooth line).

FIG. 3 shows the comparison of the theoretical spectral curves (linewith data points) that would result by using the matched coatingcomposition containing the preliminary colorant combinations of Formula2 with the measured spectral curve from the target portion of the targetcoating (solid smooth line).

FIG. 4 shows the comparison of the theoretical spectral curves (linewith data points) that would result by using the matched coatingcomposition containing the preliminary colorant combinations of Formula3 with the measured spectral curve from the target portion of the targetcoating (solid smooth line).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The terms stated herein are as defined in ASTM Publication designated asE 284-03a, which is published ASTM International, West Conshohocken,Pa.:

Angle of illumination, angle between the specimen normal and theilluminator axis (1991).

Angle of incidence—the angle between a ray impinging on a surface at apoint and the perpendicular to the surface at that point. In thedescription of a beam, the angle of incidence of the ray at the centerof the beam.

Absorption coefficient, α, —measure of the absorption of radiant energyfrom an incident beam (P₀) as it traverses an absorbing medium accordingto Bouguer's law, P=P₀e^(−αb) where b is the sample optical path length(1988).

Angle of reflection, the angle between a ray reflected from a surface ata point and the perpendicular to the surface at that point.

Angle of view, angle between the normal to the surface of the specimenand the axis of the receiver (1988).

Appearance, (1) the aspect of visual experience by which things arerecognized. (1990) (2) in psychophysical studies, perception in whichthe spectral and geometric aspects of a visual stimulus are integratedwith its illuminating and viewing environment (1993).

Artificial daylight, an artificial light that has a spectral powerdistribution approximating that of a phase of natural daylight (1995).

Aspecular, away from the specular direction (1995).

Aspecular angle, viewing angle measured from the specular direction, inthe illuminator plane unless otherwise specified (1995). Note-Positivevalues of the aspecular angle are in the direction toward theilluminator axis.

Attributes of color—(1) for the object mode of appearance, hue,lightness, and saturation. In the Munsell system, Munsell Hue, MunsellValue, and Munsell Chroma. (2) for the illuminant or aperture mode, hue,brightness, and saturation.

Basic color terms, a group of eleven color names found inanthropological surveys to be in wide use in fully developed languages:white, black, red, green, yellow, blue, brown, gray, orange, purple,pink (1990).

Characterize, means to specify the parameters or performance of aninstrument or method of measurement. For example, in appearancemeasurement, the parameters might include the geometric and spectralnature of the illuminator and the receiver, and the performance might bespecified by measures of reliability, precision, and bias (1994).

Chroma, (1) attribute of color used to indicate the degree of departureof the color from a gray of the same lightness. See also Munsell chroma(1989). (2) C*, (in the CIE 1976 L*, a*, b* or L*, u* v* system) thequantityC*ab=(a* ² +b*2)^(1/2) or C* _(uv)=(u* ² +v*2)^(1/2) (1989).

(3) attribute of a visual perception, produced by an object color thatpermits a judgment to be made of the amount of pure chromatic colorpresent, irrespective of the amount of achromatic color (1995).

CIE, the abbreviation for the French title of the InternationalCommission on Illumination, Commission Internationale de I″Eclairage.

CIE Spectral tristimulus values, n tristimulus values or color-matchingfunctions of the spectral components of an equal-energy spectrum in theCIE (XYZ) system. The color matching functions are assigned the symbolsx(λ), y(λ), z(λ) in the CIE 1931 calorimetric system and x ₁₀, (λ), y₁₀(λ) z ₁₀(λ) in the CIE 1964 supplementary calorimetric system (1990).

CIE 1964 (x₁₀, y_(io)) chromaticity diagram, n-chromaticity diagram forthe CIE 1964 supplementary standard observer, in which the CIE 1964chromaticity coordinates are plotted, with x₁₀ as abscissa and y₁₀ asordinate (1993).

Color, (1) of an object, aspect of object appearance distinct from form,shape, size, position, or gloss that depends upon the spectralcomposition of the incident light, the spectral reflectance ortransmittance of the object, and the spectral, response of the observer,as well as the illuminating and viewing geometry. (1987) (2) perceived,attribute of visual perception that can be described by color names suchas white, gray, black, yellow, brown, vivid red, deep reddish purple, orby combinations of such names. Perceived color depends greatly on thespectral power distribution of the color stimulus, but also on the size,shape, structure, and surround of the stimulus area, the state ofadaptation of the observer's visual system, and the observers experiencewith similar observations.

(3) calorimetric, characteristics of a color stimulus denoted by acolorimetric specification with three values, such as tristimulusvalues. Tristimulus values are sometimes derived on a relative ratherthan an absolute basis. In this case they may need to be supplemented bythe value of a suitable absolute photometric quantity. The appearance ofcolors depends not only on their absolute tristimulus values, but alsoon the conditions under which they are viewed, including the nature ofthe surround; however, colors having the same absolute tristimulusvalues appear the same in identical viewing conditions. Spectrallydifferent color stimuli can have the same absolute tristimulus values.

Color difference, (1) perceived, the magnitude and character of thedifference between two colors described by such terms as redder, bluer,lighter, darker, grayer, or cleaner. (2) computed, the magnitude anddirection of the difference between two psychophysical color stimuli andtheir components computed from tristimulus values, or chromaticitycoordinates and luminance factor, by means of a specified set ofcolor-difference equations

Color match, (1) condition existing when colors match within a specifiedor agreed tolerance. Sometimes called commercial color match. Compliancewith tolerances can be determined instrumentally or visually. If thetest for compliance is visual, physical color tolerance standards may beused for reference. (2) condition existing when colors areindistinguishable; a normal observer is usually implied. Sometimescalled an exact color match (1988)

Color matching, procedure for providing, by selection, formulation,adjustment, or other means, a trial color that is indistinguishablefrom, or within specified tolerances of, a specified standard colorunder specified conditions (1988).

Complementary colors, color stimuli that produce a specified achromaticstimulus when they are suitably mixed in an additive manner.

Gloss, angular selectivity of reflectance, involving surface-reflectedlight, responsible for the degree to which reflected highlights orimages of objects may be seen as superimposed on a surface. (See alsodistinctness-of-image gloss, haze (in reflection), luster, sheen,specular gloss.)

Gonioapparent, pertaining to change in appearance with change inillumination angle or viewing angle.

Hiding power, (1) the ability of a coating material to hide the surfacecoated by producing a specified opacity. (2) the area over which aspecified volume of paint can be spread to produce a specified contrast,C_(c), between areas where the substrate is black and where it is white.

Illuminant, radiant flux that may be specified by its spectral powerdistribution, and that can, in illuminating objects, affect theirperceived colors.

Match, means to provide, by selection, formulation, adjustment, or othermeans, a trial color that is indistinguishable from, or within specifiedtolerances of, a specified standard color under specified conditions(1991).

Metallic, pertaining to the appearance of a gonioapparent materialcontaining metal flakes.

Metameric, (1) pertaining to spectrally different objects or colorstimuli that have the same tristimulus values (1988). (2) pertaining toobjects, having different spectrophotometric curves that match whenilluminated by at least one specific spectral composition and observedby a specific observer. (See also parameric) (1988).

Metamerism, property of two specimens that match under a specifiedilluminator and to a specified observer and whose spectral reflectancesor transmittances differ in the visible wavelengths. See also illuminantmetamerism, observer metamerism, paramerism. As a consequence of therequired difference, the two specimens may not match under a differentilluminator or to a different observer. Similar considerations apply totwo lights matching to a specified observer but not to other observers,metamerism indices (1991).

Metamers, (1) spectrally different objects or color stimuli _(c) thathave the same—stimulus values (1988).

Reflectance, ρ, ratio of the reflected radiant or luminous flux to theincident flux in the given conditions. The term reflectance is oftenused in a general sense or as an abbreviation for reflectance factor.Such usage may be assumed unless the above definition is specificallyrequired by the context (1989).

Shade, (1) a color produced by a dye or pigment mixture including blackdye or pigment. See also shade, v; tint, n; tint, v. (2) an expressionof color difference from a reference dyeing such that another dye mustbe added to produce a match. (3) a color slightly different from areference color. “Shade” is the most overworked of the terms used todescribe colors and color differences in terms of colorant technology,sometimes even being used as a general synonym for “color.”

Shade, means to adjust the color of a test specimen to be a closer colormatch to the standard. Also tint (1990).

Spectral, (1) modifying a quantity, descriptor that the quantity is afunction of wavelength; (2) for radiometric quantities, pertaining tomonochromatic radiant energy at a specified wavelength or, by extension,to radiant energy within a narrow wavelength band about a specifiedwave-length.

Spectrophotometry, quantitative measurement of reflection ortransmission properties as a function of wavelength.

Specular, pertaining to flux reflected from the surface of an object,without diffusion, at the specular angle (1988).

Specular angle, n-the angle of reflection equal and opposite to theangle of incidence. In gonioapparent phenomena, this definition assumesan illuminator subtending a small angle (1995).

Tint, a color produced by the mixture of white pigment or paint with achromatic pigment or paint. A tint of a chromatic color is, therefore,lighter and less saturated than the chromatic color. (See shade)

Tristimulus values-amounts of three specified stimuli required to matcha color. In the CIE system, they are assigned the symbols X, Y, and Z.(See also CIE spectral tristimulus values.)

Viewing conditions, the conditions under which a visual observation ismade, including the angular subtense of the specimen at the eye, thegeometric relationship of source, specimen, and eye, the photometric andspectral character of the source, the photometric and spectral characterof the field of view surrounding the specimen, and the state ofadaptation of the eye.

Wavelength, X of an electromagnetic wave, the distance in the directionof propagation between nearest points at which the electric vector hasthe same phase (See also complementary wavelength, dominant wavelength)(1990).

The present invention is suited to expeditiously color match the targetcoating, such as an undamaged portion of an autobody, in a typicalautomotive collision repair shop environment. The method of the presentinvention substantially automates the color matching process even underthe varying conditions typically experienced in the collision repairshops. In a typical collision repair shop, the d portion of an autobodyis repaired, sanded and primed before a coating composition is applied,such as by spraying, dip coating, roller coating or with a brush. Bymatching the color of a coating composition with the undamaged portionof an autobody, one can use a very small amount of matched coatingcomposition to paint the repaired portion of the autobody. As a result,the cost of auto repair can be minimized while still visually matchingthe repaired portion of the autobody with the undamaged portion of theautobody.

Broadly stated, in the method of the present invention, the color of thetarget coating is read by a spectrophotometer (preferably portable), thespectral measurement is transmitted to a computer, an optimum paintformula is determined with the pigment mixture models and printed out ordisplayed on the computer screen for the shop to weigh and spray. Allsteps between the measurement and the receipt of the formula aretransparent to the user.

While this invention is preferably used in a refinish auto body shop, itcan be also used for color matching in other suitable areas, such asmatching coatings on plastic substrates or colored plastic substrates;marine substrates, such as ship hulls; aluminum substrates, such asaircraft bodies, matching architectural coatings; textile fibers,fabrics, and non-woven fabrics; and on paper. It could also be used in alaboratory environment with a less skilled work force. The portabilityof the device of the present invention makes the invention ideal for usein the field.

A method of the present invention is directed to producing a matchedcoating composition for a specified end-use that visually matches inappearance with a target portion of the target coating. Some of thespecified uses can include automotive refinish coatings applied overautobodies, automotive OEM finishes, architectural coatings, industrialcoatings, powder coatings, aviation coatings, marine coatings,commercial and residential appliances coatings. The foregoing includescoatings applied over a variety of substrates, such as steel, aluminum,wood, plastic resins, glass, paper, textile fibers, fabrics, non-wovenfabrics and cement.

Step (i) of the method of the present invention includes measuringreflectances of a target portion of a target coating applied by means ofa spectrophotometer of a coating characterizing device of the presentinvention. Any suitable spectrophotometer, such as Model MA68II or ModelSP64 manufactured by X-Rite, Grandville, Mich. can be used. Portablespectrophotometers are preferred as they can be readily positioned overcoated substrate surfaces of various shapes and sizes. If desired onecan measure the reflectances over several portions of the target coatingto average out the reflectances of the target coating. In a typicalspectrophotometer, a light beam of known intensity can be directedtowards the target portion and reflectance from the target potion issequentially measured at at least one, preferably at three, aspecularangles at preset wavelengths. Alternatively, a light beam of knownintensity can be sequentially directed at at least one, preferably atthree, incident angles towards the target portion and reflectance fromthe target portion is then measured at preset wavelengths with a singledetecting device so as to provide measurements at different aspecularangles, depending on the angle of illumination. Gonioapparent colorsshould be measured at multiple angles, preferably 3 to 5. For solidcolors, a single aspecular angle is sufficient, typically 45 degrees. Acommon practice for solid colors is to illuminate at a single angle andmeasure the diffuse reflectance using an integrating sphere, capturingthe light reflected at all angles from the target portion. The reversemethod of illuminating diffusely and measuring at a single angle yieldsequivalent results. Diffuse reflectance is preferred when the targetportion has a textured surface.

Color has long been measured through the use of spectrophotometers,which measure the percentage of light reflected at each wavelength overthe visible region of the electromagnetic spectrum. Typically thesereadings are taken at 10 nm intervals from 400 nm to 700 nm. A plot ofthe percent reflectance as a function of wavelength is referred to as a“spectral curve”. By way of example, Table 1 shows reflectances of thetarget portion measured at wavelengths in visible spectrum, ranging from400 nanometers to 700 nanometers at 10 nanometer intervals with anX-Rite MA68II spectrophotometer wherein the target portion wasilluminated at 45° to the normal and the reflectance was measured at thenormal angle. For a solid color (non-flake or non-gonioapparent color,such as that lacking metallic flakes), only one spectral curve istypically sufficient to measure solid color properties. Other commongeometries of measurement are diffuse illumination with 0° or 8° viewingor the reverse. If a target portion having a metallic color, i.e.,gonioapparent color was being matched, reflectance measurements atadditional angles would be necessary. ASTM E-2194 recommends threeangles, 15°, 45°, and 110° as measured away from the specularreflection. DIN 6175-2 recommends up to five angles, all within thissame range of angles. The X-Rite MA68II can provide measurements at 15°,25°, 45°, 75°, and 110°.

Step (ii) of the method of the present invention comprises calculatingtarget color values of the target portion from the target spectral curveof the target portion. Several alternate equations have been developedto reduce spectral values to numbers indicative of the way a humanobserver sees the color under a given lighting condition. These arecommonly expressed as L,a,b or L,C,h values.

From a spectral curve, one can determine the hue of a color representedby the peak of the curve, e.g., the spectral curve of a blue color wouldpeak in blue wavelengths. A light color would reflect more light acrossthe spectrum and a darker color would reflect less light. A high chromacolor would have a reasonably sharper peak and reflect considerably lesslight at other wavelengths. A low chroma color would have a curve withlittle difference between peak and trough. Grays would tend to be veryflat. Thus a qualitative assessment of the color is possible from aspectral curve. However, color as seen by a human observer is dependentnot only on the spectral curve of the color but also the spectralcharacteristics of the light source under which it is viewed and thespectral sensitivity of the observer. The human eye has three sensorsfor color vision-a red sensor (X), a green sensor (Y) and a blue sensor(Z). In 1931, the International Committee on Illumination (CIE)standardized the mapping of color in a three-dimensional X, Y, Z space,allowing for the spectral characteristics of the color, the light sourceand the observer. However it is still difficult to visualize a colorfrom its tristimulus values X, Y, Z. Also, these values do not provide avisually uniform three-dimensional mapping of color. The tristimulusvalues X, Y, Z can be calculated though the following matrix equation:t= TER  (A)

t=vector of tristimulus values X, Y, Z

T=vector of standard observer weighting functions, which can be obtainedfrom E-308 publication of the American Society of Testing & Materials(ASTM).

Ē=vector of relative spectral energy distribution of the light sourcefunctions, which can be obtained from ASTM E-308. Illuminant D₆₅,representing daylight is commonly used.

R=vector of reflectance values

The foregoing X, Y and Z tristimulus values can be more convenientlyexpressed by using mathematical transformations to “uniform color space”known as L,a,b values, which are described in Theory and Implementationof Modern Techniques of Color Conception, Matching and Control by A. B.J. Rodrigues at Fifth International Conference in Organic CoatingsScience and Technology Proceedings, Vol. 3, Advances in Organic CoatingsScience and Technology Series, p. 273-275, (1979). The aforementionedreference is hereby incorporated herein by reference. The L,a,b valuesof the color describes the position of the color. The L,a,b values ofeach color are a three dimensional rendering of color space in Cartesiancoordinates in which a Lightness axis (L*), a red-green axis (a*), and ayellow-blue axis (b*), are described by the following equations:L*=116(Y/Y ₀)⅓−16   (1)a*=500[(X/X ₀)⅓−(Y/Y ₀)⅓]  (2)b*=200[(Y/Y ₀)⅓−(Z/Z ₀)⅓]  (3)

For X/X₀, Y/Y₀, Z/Z₀>0.008856 (For D₆₅ at 10°, X₀=94.825, Y₀=100.000 andZ₀=107.381).

For X/X₀, Y/Y₀, Z/Z₀<0.008856, L*=903.3 (Y/Y₀).

The cube root functions in the equations for a*, b* are replaced by thefollowing corresponding functions:f(X/X ₀)=7.787(X/X ₀)+0.1379f(Y/Y ₀)=7.787(Y/Y ₀)+0.1379f(Z/Z ₀)=7.787(Z/Z ₀)+0.1379

In the foregoing equations, X₀, Y₀ and Z₀ are the tristimulus values ofa perfect white color for a given illuminant; and X, Y and Z are thetristimulus values for the color to be evaluated. Thus, the L,a,b valuesare obtained by mathematically integrating the spectral reflectancecurve of the color with the spectral distribution of the light source,typically, Illuminant D65, and the spectral sensitivities of thereceptors in the human eye, all published in tables listed in ASTMStandard E-308. The foregoing integration process allows characterizingthe color through three parameters, generally referred to by X, Y, andZ. The foregoing mathematical transformations readily allow conversionof X, Y, Z to the easier to understand L,a,b values.

Table 1 below shows the spectral reflectance and the L, a, b values ofthe color of the target portion. L=30.62 indicates that it was a mediumto dark color; a=49.87 indicates that it was a fairly saturated red andb=28.57 indicates that it had a yellow shade red.

TABLE 1 Wavelength Reflectance of in nanometers Target Portion 4000.0320 410 0.0330 420 0.0290 430 0.0250 440 0.0200 450 0.0160 460 0.0140470 0.0120 480 0.0110 490 0.0100 500 0.0098 510 0.0098 520 0.0098 5300.0100 540 0.0100 550 0.0110 560 0.0130 570 0.0180 580 0.0370 590 0.0960600 0.1880 610 0.2730 620 0.3240 630 0.3500 640 0.3650 650 0.3730 6600.3790 670 0.3820 680 0.3840 690 0.3860 700 0.3870 L 30.62 a 49.87 b28.57

An acceptable alternative to L,a,b values are the L,C,h values obtainedby transforming the color values expressed in Cartesian coordinates intocylindrical coordinates to provide more accurate and uniformrepresentation of the color difference (ΔE) between the target color andthe color that matches the target color by using CIE94 or CMC equation.These equations are known and are disclosed in Berns, R. S., “Billmeyerand Saltzman's Principles of Color Technology”, 3^(rd). Ed., pgs.120-121, and pages. 117-118, John Wiley & Sons, Inc., which isincorporated herein by reference. The CIE94 equation utilizes the L,a,bvalues and converts them into the L,C,h values by using the followingequations.

L,a,b for target coating and matched compositions can be calculated byusing Equations 1, 2 and 3, and color differences ΔL, Δa, Δb aredetermined by taking into account the differences between the targetcoating and matched coating. These differences may be determined fordifferent light sources. In L,C,h values, the “C” is determined by theequation below:Chroma=C*=√{square root over (a* ² +b* ²)}  (4)and the “h” value is determined by the equation below:Hue=h=tan⁻¹(b*/a*)  (5)

h is also known as the hue angle

Differences in the color of the target and matched coating are expressedas:ΔL*=L* _(b) −L* _(s)Δa*=a* _(b) −a* _(s)Δb*=b* _(b) −b* _(s)ΔC*=C* _(b) −C* _(s)(subscripts s and b in the foregoing equations refer to the target andmatched coatings).

Total color difference ΔE* between the target and matched coatings isgiven by:ΔE*=√{square root over (ΔL* ² +Δa* ² +Δb* ²)}  (6)ΔH*=k√{square root over (ΔE* ² −ΔL* ² −ΔC* ²)} (Also referred to as themetric hue difference).

The general equation that expresses the color difference between thetarget and matched coatings is given by:

$\begin{matrix}{{\Delta\; E} = \left\lbrack {\left( \frac{\Delta\; L^{*}}{K_{L}S_{L}} \right)^{2} + \left( \frac{\Delta\; C_{ab}^{*}}{K_{C}S_{C}} \right)^{2} + \left( \frac{\Delta\; H_{ab}^{*}}{K_{H}S_{H}} \right)^{2}} \right\rbrack^{0.5}} & (7)\end{matrix}$

Several alternatives have been developed to solve Equation 7 forobtaining L,C,h values, such as, for example, the well known CIE 94 andCMC equations described below:

CIE94 Equation The CMC Equations CR&A, 18, 137-139(1993)For solidcolors: S_(L) = 1.0${{{For}\mspace{14mu} L\;*} > {16\mspace{14mu} S_{L}}} = \frac{0.040975L*}{1 + {0.01765L*}}$For metallic colors: S_(L) = 0.034L*; If L* ≦ 29.4., S_(L) = 1.0 for L*≦ 16 S_(L) = 0.511 S_(C) = 1 + 0.045C*_(ab)where C*_(ab) is that of thestandard$S_{C} = {\frac{0.0638C_{ab}^{*}}{1 + {0.0131C_{ab}^{*}}} + 0.638}$S_(H) = (FT + 1 − F) S_(C) S_(H) = 1 + 0.015C*_(ab) where The parametricfactors K_(L):K_(C):K_(H) =1:1:1 are generally satisfactory.However, iflightness is of lesserimportance, K_(L):K_(C):K_(H) can beequal to2:1:1.For metallic color S_(L) function isprovided in Rodrigues A. B.J.,Locke, J. S., SPIE Vol. 4421,Editors Robert Chung & AllanRodrigues,pgs 658-661, which isincorporated herein by reference. $\begin{matrix}{F = \left\lbrack \frac{\left( C_{ab}^{*} \right)^{4}}{\left( C_{ab}^{*} \right)^{4} + 1900} \right\rbrack^{0.5}} \\{S_{L} = \frac{0.040975L*}{1 + {0.01765L*}}} \\{and} \\{T = {0.36 + {{abs}\left\lbrack {0.4\mspace{14mu}\cos\mspace{11mu}\left( {35 + h_{ab}} \right)} \right\rbrack}}} \\{{unless}\mspace{14mu} h\mspace{14mu}{is}\mspace{14mu}{between}\mspace{14mu} 164{^\circ}\mspace{11mu}{and}\mspace{14mu} 345{^\circ}} \\{then} \\{T = {0.56 + {{abs}\left\lbrack {0.2\mspace{11mu}\cos\mspace{11mu}\left( {168 + h_{ab}} \right)} \right\rbrack}}}\end{matrix}\quad$

It should be noted that even other equations have been developed andcontinue to be developed for obtaining the L,a,b or L,C,h and ΔE valuesof color from the measurements of the reflectances of target portion andΔE for the color difference. The method of the present invention is notbound to any specific equations.

Once the target values of a color of the target portion are determined,step (iii) of the method of the present invention comprises selectingone or more preliminary colorant combinations from a stored list ofknown colorants in accordance with combinatorial selection criteria tomatch with said target color values.

There are many ways to create the aforementioned stored list of thecolorants. The stored list preferably includes all colorants, such aspigments, dispersions, tints, dyes, metallic flakes (colored aluminumflakes) or a combination thereof that may be needed to produce thematched composition. Each colorant is associated with a database ofoptical coefficients. Generally, one can produce a matched coatingcomposition by adjusting the concentration in a mixture of severalcolorants of known optical coefficients that would produce a spectralcurve that matches the spectral curve of the target portion. The opticalcoefficients typically include absorption (K) and scattering (S)coefficients, which can be used in a pigment mixture model (e.g.,Kubelka-Munk and others based on radiative transfer theory) to relatepigment mixture concentrations to spectral curve(s) for that mixture.

The well known Kubelka-Munk model relates reflectance at complete hidingto absorption and scattering coefficients for the colorant, typicallyapplied at preset wavelength intervals over the visible spectrum,typically at intervals of 10 nm:K/S=(1−R)²/2R  (8)

where K=absorption coefficient, which is an indicator of a coatingmaterial's internal absorptance.

S=scattering coefficient, which is the portion of light scattered whentraveling through a unit thickness of the coating material; and

R=reflectance at complete hiding of the coating material. Thereflectance values determined at each wavelength at 10 nanometerintervals of the coating on the target portion are shown in Table 1. TheK/S value for a mixture of colorants can be expressed through thefollowing equation:(K/S)_(mix)=(c ₁ K ₁ +c ₂ K ₂+ . . . )/(c ₁ S ₁ +c ₂ S ₂+ . . . )  (9)

where c=concentration and 1, 2 refer to colorants 1, 2, etc. present inthe colorants mixture.

A test coating composition containing a light colorant, such as a whitecolorant (titanium dioxide pigment) can be typically used to create thedatabase. A test coating composition made from a white colorant wassprayed on a test panel to a dry coating thickness sufficient tocompletely hide the color of the panel itself, which is typically graycolored. The reflectance of the white coating was then measured atpreset wavelength intervals in the visible spectrum, typically at 10nanometer (nm) intervals starting from 400 nm to 700 nm. Anyconventional spectrophotometers, such as that supplied by X-Rite,Grandville, Mich. Model MA100B, MA68II or SP64 can be used to measurethe reflectance. Such reflectances, as a function of wavelength, arecalled the spectral reflectances or spectral curves of that whitecoating. The measured reflectance, R was substituted into Equation 8 tocalculate K/S at each wavelength. It is convenient to assign a value of1.0 to the scattering coefficients (S) of white colorant at eachwavelength. Thus, substituting S=1.0 provides the value for K.

For example, Table 2 below reports reflectances of a white test coatingcomposition measured at wavelengths ranging from 400 nm to 700 nm at 10nm intervals. The colorant used in the white coating composition wastitanium dioxide. In Table 2, the measured reflectance of the whitecoating at 420 nm is 77.28%. Substituting R=0.7728 into Equation 8 gaveK/S=0.0334. Since S=1.0, K would be 0.0334. Similarly, K can becalculated at each wavelength. The results for K/S are reported in the“100% White, K/S” column of Table 2. The separate K and S values for thewhite are shown in Table 3 later.

A coating composition containing a mixture of 50% black and 50% whitewas made into paint, sprayed, and its reflectance measured at eachwavelength. Another paint that was 100% black was similarly sprayed andmeasured. The black coating composition was pigmented with carbon black.These measurements are reported in Table 2, along with the correspondingK/S values calculated by Equation 8.

TABLE 2 50/50 Colorant 100% White 100% Black White/Black Nms R K/S R K/SR K/S wl_400 0.3404 0.6391 0.0023 220.4118 0.2661 1.0121 wl_410 0.58980.1426 0.0027 182.8000 0.3795 0.5072 wl_420 0.7728 0.0334 0.0031162.1818 0.4248 0.3893 wl_430 0.8327 0.0168 0.0031 159.4091 0.43510.3667 wl_440 0.8407 0.0151 0.0031 159.9091 0.4354 0.3661 wl_450 0.84710.0138 0.0031 162.0000 0.4339 0.3694 wl_460 0.8534 0.0126 0.0032156.2174 0.4331 0.3710 wl_470 0.8588 0.0116 0.0033 150.8750 0.43230.3728 wl_480 0.8628 0.0109 0.0033 151.7500 0.4316 0.3742 wl_490 0.86700.0102 0.0032 152.9583 0.4306 0.3764 wl_500 0.8701 0.0097 0.0032153.8333 0.4299 0.3780 wl_510 0.8745 0.0090 0.0033 148.6400 0.42920.3797 wl_520 0.8785 0.0084 0.0033 149.3200 0.4287 0.3807 wl_530 0.88200.0079 0.0034 144.2692 0.4281 0.3820 wl_540 0.8841 0.0076 0.0034145.5769 0.4267 0.3851 wl_550 0.8855 0.0074 0.0034 146.4615 0.42580.3872 wl_560 0.8855 0.0074 0.0035 142.2963 0.4243 0.3905 wl_570 0.88550.0074 0.0035 143.3333 0.4231 0.3933 wl_580 0.8862 0.0073 0.0036139.0000 0.4222 0.3954 wl_590 0.8862 0.0073 0.0035 140.1072 0.42090.3985 wl_600 0.8862 0.0073 0.0036 136.1034 0.4198 0.4008 wl_610 0.88550.0074 0.0036 136.7931 0.4190 0.4029 wl_620 0.8841 0.0076 0.0037133.7333 0.4170 0.4076 wl_630 0.8827 0.0078 0.0037 135.2000 0.41510.4122 wl_640 0.8813 0.0080 0.0038 132.3226 0.4131 0.4169 wl_650 0.87990.0082 0.0038 129.2813 0.4116 0.4206 wl_660 0.8792 0.0083 0.0039126.6970 0.4098 0.4250 wl_670 0.8778 0.0085 0.0040 124.5000 0.40770.4303 wl_680 0.8765 0.0087 0.0041 122.2286 0.4058 0.4350 wl_690 0.87580.0088 0.0042 116.7297 0.4042 0.4391 wl_700 0.8758 0.0088 0.0044111.7949 0.4027 0.4431

For a binary mixture of a colorant plus white, Equation 9 can be writtenas:(K/S)_(mix)=(c _(w) K _(w) +c _(c) K _(c))/(c _(w) S _(w) +c _(c) S_(c))  (10)

At 420 nm, substituting the values of K_(w) and S_(w) in Equation (10),(K/S)_(mix)=(0.0334c _(w) +c _(c) K _(c))/(c _(w) +c _(c) S _(c))

At 420 nm the 50/50 mixture (c_(w)=c_(c)=0.5) has R=0.4248 (as shown inTable 2 above), the 100% black has R=0.0031. These are substituted intoEquation 8 to provide (K/S)_(mix) with the respective concentrations(50/50 mixture and 100% black). These (K/S)_(mix) values can be thensubstituted in Equation 8 to provide two equations, which can besimultaneously solved for the two unknowns K_(c) and S_(c), providingK_(c)=0.3568 and S_(c)=0.0022. Similarly the K and S of the black can bedetermined at each wavelength.

The same process allows determination of K and S for each of thecolorants used. These are shown in the following Tables 3 and 4, alongwith K and S values for several other colorants. It should be noted thatin practice, several blends of each colorant with white could be usedwith well known statistical procedures to determine the values of K andS.

TABLE 3 Absorption (K) and Scattering (S) Coefficients for ColorantsColorant White Black Red Oxide data_id K S K S K S wl_400 0.6391 1.00000.3747 0.0017 1.5644 0.0226 wl_410 0.1426 1.0000 0.3656 0.0020 1.55930.0244 wl_420 0.0334 1.0000 0.3568 0.0022 1.4739 0.0253 wl_430 0.01681.0000 0.3507 0.0022 1.4420 0.0263 wl_440 0.0151 1.0000 0.3518 0.00221.4792 0.0280 wl_450 0.0138 1.0000 0.3564 0.0022 1.5006 0.0296 wl_4600.0126 1.0000 0.3593 0.0023 1.5123 0.0313 wl_470 0.0116 1.0000 0.36210.0024 1.5238 0.0331 wl_480 0.0109 1.0000 0.3642 0.0024 1.5338 0.0351wl_490 0.0102 1.0000 0.3671 0.0024 1.5420 0.0378 wl_500 0.0097 1.00000.3692 0.0024 1.5417 0.0405 wl_510 0.0090 1.0000 0.3716 0.0025 1.53650.0440 wl_520 0.0084 1.0000 0.3733 0.0025 1.5258 0.0484 wl_530 0.00791.0000 0.3751 0.0026 1.4991 0.0544 wl_540 0.0076 1.0000 0.3785 0.00261.4393 0.0639 wl_550 0.0074 1.0000 0.3808 0.0026 1.3088 0.0797 wl_5600.0074 1.0000 0.3842 0.0027 1.0948 0.1036 wl_570 0.0074 1.0000 0.38700.0027 0.8291 0.1330 wl_580 0.0073 1.0000 0.3892 0.0028 0.5871 0.1594wl_590 0.0073 1.0000 0.3923 0.0028 0.4140 0.1781 wl_600 0.0073 1.00000.3947 0.0029 0.3057 0.1878 wl_610 0.0074 1.0000 0.3967 0.0029 0.24280.1916 wl_620 0.0076 1.0000 0.4012 0.0030 0.2073 0.1924 wl_630 0.00781.0000 0.4056 0.0030 0.1858 0.1924 wl_640 0.0080 1.0000 0.4102 0.00310.1692 0.1909 wl_650 0.0082 1.0000 0.4137 0.0032 0.1553 0.1908 wl_6600.0083 1.0000 0.4181 0.0033 0.1418 0.1900 wl_670 0.0085 1.0000 0.42330.0034 0.1289 0.1900 wl_680 0.0087 1.0000 0.4278 0.0035 0.1156 0.1897wl_690 0.0088 1.0000 0.4319 0.0037 0.1028 0.1896 wl_700 0.0088 1.00000.4360 0.0039 0.0910 0.1887

TABLE 4 Absorption (K) and Scattering (S) Coefficients for ColorantsColorant Red 1 Yellow Red 2 Red 3 data_id K S K S K S K S wl_400 1.36810.1169 3.4994 0.0134 2.1550 0.0084 0.5906 0.0182 wl_410 1.2546 0.11053.7703 0.0143 2.0614 0.0085 0.5432 0.0168 wl_420 1.3386 0.0981 4.05210.0182 2.7665 0.0135 0.5245 0.0149 wl_430 1.5478 0.0837 4.4643 0.02394.3506 0.0261 0.5650 0.0132 wl_440 1.9097 0.0698 5.0305 0.0321 6.17080.0411 0.6865 0.0122 wl_450 2.3670 0.0596 5.5365 0.0409 7.9914 0.05620.8568 0.0114 wl_460 2.8360 0.0538 6.0349 0.0507 9.2974 0.0687 1.06270.0107 wl_470 3.3776 0.0506 6.4970 0.0590 10.0134 0.0777 1.3954 0.0104wl_480 4.0108 0.0499 6.8039 0.0617 10.0540 0.0806 1.8751 0.0106 wl_4904.4932 0.0532 7.1009 0.0686 9.6639 0.0794 2.3086 0.0113 wl_500 4.71930.0538 7.4505 0.0787 9.0982 0.0792 3.0752 0.0133 wl_510 5.2135 0.06067.8757 0.0887 8.0685 0.0759 4.1112 0.0169 wl_520 5.7929 0.0722 8.04990.0847 7.0089 0.0679 4.9350 0.0203 wl_530 6.0009 0.0772 8.1088 0.08016.2570 0.0605 5.2736 0.0229 wl_540 5.9758 0.0783 8.7268 0.1045 6.27710.0578 5.0901 0.0249 wl_550 6.2267 0.0877 9.7953 0.1577 6.4474 0.06284.6297 0.0273 wl_560 6.4646 0.1154 10.6382 0.2081 5.6369 0.0695 3.63710.0300 wl_570 5.6608 0.1585 10.2559 0.2510 3.9603 0.0726 2.3551 0.0294wl_580 3.5909 0.2118 7.1849 0.3638 2.2508 0.0695 1.1276 0.0262 wl_5901.7339 0.2655 3.0326 0.5296 1.1697 0.0635 0.4224 0.0234 wl_600 0.60620.2886 0.6601 0.5904 0.6004 0.0581 0.1963 0.0214 wl_610 0.2789 0.28130.2411 0.5344 0.3244 0.0548 0.1045 0.0198 wl_620 0.1574 0.2652 0.10460.4752 0.1901 0.0526 0.0679 0.0187 wl_630 0.1055 0.2522 0.0526 0.43150.1244 0.0510 0.0520 0.0178 wl_640 0.0736 0.2427 0.0327 0.3986 0.09210.0490 0.0444 0.0170 wl_650 0.0560 0.2364 0.0247 0.3752 0.0756 0.04700.0403 0.0165 wl_660 0.0440 0.2293 0.0204 0.3572 0.0660 0.0449 0.03810.0158 wl_670 0.0379 0.2231 0.0174 0.3424 0.0594 0.0432 0.0391 0.0154wl_680 0.0341 0.2162 0.0152 0.3302 0.0545 0.0417 0.0446 0.0150 wl_6900.0318 0.2106 0.0138 0.3200 0.0511 0.0403 0.0465 0.0146 wl_700 0.03000.2038 0.0127 0.3114 0.0488 0.0388 0.0411 0.0145

The combinatorial selection criteria on which one or more preliminarycolorant combinations from the stored list of known colorants that matchwith the target color values are selected are for their practicality,i.e., is it practical to make such preliminary combinations? By way ofexample, assume a case where the colorants used are White (W), Black(B), Red Oxide (RO), Yellow (Y), Red 1 (R1), Red 2 (R2), Red 3 (R3), andit is desired to have a 5-pigment match. It is customary, though notessential to include W and B in each colorant combination attempted. Allcombinations of the remaining five colorants are taken, three at a time,with W and B to attempt a match. Such a process provides ten possible5-pigment combinatorial selection criteria:

-   -   W, B, RO, Y, R1    -   W, B, RO, Y, R2    -   W, B, RO, Y, R3    -   W, B, RO, R1, R2    -   W, B, RO, R1, R3    -   W, B, RO, R2, R3    -   W, B, Y, R1, R2    -   W, B, Y, R1, R3    -   W, B, Y, R2, R3    -   W, B, R1, R2, R3

By way of example, if a target portion is red, the preliminarycombination should not include green, since that combination wouldresult in shading (adjusting) with two complementary colorants. However,red and green together can be used to desaturate and darken the color.The same result can be obtained by using black, which is generally aless expensive colorant. Hence, the normal practice is to avoid shadingwith complementary colorants.

For solid colors (non-flake) it is preferable to start with 4-colorantcombinatorial selection criteria to ascertain whether the resultingcolor match could be improved with five or six colorants. Preferably,the fewer the number of pigments, the more practical is the resultantpreliminary combination, since, a typical refinish body shop wouldrequire less time to weigh a 4-colorant automotive paint than a 5- or6-colorant automotive paint.

Thus, by way of example, from the stored list shown in Tables 2, 3 and4, the following selected formulas, shown in Table 5 below, would meetthe aforedescribed combinatorial selection criteria and also come closeto matching the target color values and reflectances. Table 5 reportsthree preliminary colorant combinations (Formulas 1, 2 and 3) selectedon the basis of the combinatorial selection criteria from the storedlist that match the target color values and reflectances:

TABLE 5 Wavelength in nm Target Formula 1 Formula 2 Formula 3 400 0.03200.0300 0.0260 0.0320 410 0.0330 0.0310 0.0290 0.0310 420 0.0290 0.02800.0270 0.0250 430 0.0250 0.0240 0.0250 0.0190 440 0.0200 0.0200 0.02200.0160 450 0.0160 0.0160 0.0200 0.0130 460 0.0140 0.0140 0.0180 0.0130470 0.0120 0.0120 0.0150 0.0120 480 0.0110 0.0110 0.0130 0.0120 4900.0100 0.0100 0.0120 0.0120 500 0.0098 0.0100 0.0110 0.0120 510 0.00980.0100 0.0087 0.0130 520 0.0098 0.0098 0.0076 0.0140 530 0.0100 0.01000.0077 0.0140 540 0.0100 0.0110 0.0082 0.0140 550 0.0110 0.0120 0.00870.0140 560 0.0130 0.0140 0.0110 0.0160 570 0.0180 0.0180 0.0180 0.0210580 0.0370 0.0350 0.0390 0.0370 590 0.0960 0.0940 0.1000 0.1000 6000.1880 0.1850 0.1970 0.1880 610 0.2730 0.2710 0.2760 0.2670 620 0.32400.3240 0.3250 0.3240 630 0.3500 0.3510 0.3550 0.3570 640 0.3650 0.36700.3700 0.3720 650 0.3730 0.3770 0.3800 0.3780 660 0.3790 0.3830 0.38500.3800 670 0.3820 0.3870 0.3810 0.3830 680 0.3840 0.3890 0.3760 0.3830690 0.3860 0.3890 0.3780 0.3810 700 0.3870 0.3890 0.3830 0.3790 L 30.6230.55 30.74 31.13 a 49.87 49.78 50.77 48.2 b 28.57 28.45 26.68 31.49

FIGS. 2 through 4 compare the theoretical spectral curves (line withdata points) that would result by using the matched coating compositionscontaining the preliminary colorant combinations of Formula 1 of FIG. 2,Formula 2 of FIG. 3 and Formula 3 of FIG. 4 with the measured spectralcurve from the target portion of the target coating (solid smooth line).

Once the preliminary colorant combinations from a stored list of knowncolorants are selected, in step (iv) of the method of the presentinvention, concentrations of each of the known colorants in each of thepreliminary colorant combinations are determined in accordance withcolor matching criteria wherein the concentration of each the knowncolorant is optimized for optimal match of color values of each of thepreliminary colorant combinations with the target color values.

The color matching criteria under which the concentrations of each ofthe known colorants in the preliminary colorant combinations can beobtained are described by E. A. Allen, Basic equations used in computercolor matching, J. Opt. Soc. Am., 56, 1256-1259 (1966), which isincorporated herein by reference (hereafter the Allen I reference). Itshould be noted that the color matching criteria could be configured toeliminate formulas with negative concentrations. In order to make anaccurate color match between the target coating with that of a matchedcoating resulting from the matched coating composition, theconcentrations of the colorants in the preliminary colorant combinationsshould generate spectral curves that would closely match with thespectral curve of the target coating. The foregoing can be accomplishedby a simple trial-and-error process, guessing at suitable pigmentcombinations and concentrations, and by using Equation 9 to calculatethe K/S of the mixture at each wavelength. Equation 8 can then be usedto convert the K/S of the mixture to its reflectance (R). The resultantspectral curve can be compared to the target spectral curve for a degreeof match. If the general shapes of the curves are similar, the rightcolorants have been chosen. The concentrations then must be adjusted tobring the curves even closer together. The closeness of the spectralcurve match could also be judged by calculating the L,a,b values of thematch. Such an iterative process can be repeated until the difference inthe L,a,b values between the known colorant mixture to the one in thetarget coating is small. However, such a process would be tedious andtime consuming. Moreover, it does it lend itself to automation. Thefollowing color matching equation in the aforenoted Allen I referencetransformed the color matching equations, allows for a direct solutionfor concentrations of each known colorant in each of the preliminarycolorant combinations by working with a combined K/S ratio rather thanseparating K and S:C =( TĒ D Φ)⁻¹ TĒ D[ f ^((s)) − f ^((t))]  (11)where C=vector of concentrations of each known colorant in each of thepreliminary colorant combinations.

T=matrix of standard observer weighting functions, which can be obtainedfrom E-308 publication of the American Society of Testing & Materials(ASTM).

Ē=vector of relative spectral energy distribution of the light sourcefunctions, which can be obtained from ASTM E-308. Illuminant D₆₅,representing daylight is commonly used.

D=matrix of dR/d(K/S) functions obtained by calculating the partialderivative of Equation 8 yielding dR/d(K/S)=−2R²/(1−R²).

Φ=matrix of K/S values for all colorants in each of the preliminarycolorant combinations.

f ^((t))=vector of K/S for target portion (t).

f ⁽¹⁾=vector of K/S for underlying substrate in case of dye mixtures orthat of white colorant for pastel shade coating compositions.

Equation 11 works well for dye mixtures on substrates; such as textilesbecause dyes typically have high absorption coefficients (K) but lowscattering coefficients (S) while the substrate on which the dyes areapplied typically has high scattering coefficients (S) but lowabsorption coefficients (K), i.e., Equation 11 would be valid for pastelshade paints with large amounts of highly scattering titanium dioxidepigment and much lower quantities of strongly absorbing pigments.

The concentrations provided by Equation 11 are useful when the colorantcombination chosen allows for a non-metameric match. When the colorantcombination chosen allows only a metameric match, the concentrationsprovided by Equation 11 can be iteratively adjusted to a metameric matchacceptably low in color difference from the target color. However, yetanother approach can be used for non-pastel color, which is reported inE. A. Allen in Basic Equations used in computer color matching, II.Tristmulus matching, two-constant theory, J. Opt. Soc. Am. 64, 991-993(1974), (hereafter Allen II reference).

Still another approach was provided by Rodrigues (7th Congress of theInternational Colour Association (AIC), Budapest, June 1993 (hereafterthe Rodrigues reference) though the following matrix equation:C =( TĒ D ψ )⁻¹ TĒ D θ ₁  (12)where

ψ_(j)=K_(j)−K₁−θ_(s)(S_(j)−S₁) for each wavelength,

θ_(t)=(K/S)_(t), and

θ₁=ψ_(j) where K_(j)=S_(j)=0.

Subscript j refers to colorant j in a group of colorants in thepreliminary colorant combinations and 1 refers to colorant 1 in thepreliminary colorant combinations and subscript t refers to the targetcoating.

When the colorants chosen allow for a non-metameric match, Equation 12provides for concentrations for a close color match. However, similar toEquation 11, Equation 12 provides for only an approximate match when thecolorants chosen allow for only a metameric match. To improve the matchin Equation 12, the concentrations of colorants in the matchedcomposition can be iteratively adjusted to provide for an acceptablematch by using the following matrix equation:ΔC =( TEDψ′ )⁻¹ Δt   (13)where,

ψ′_(j)=ψ_(j)/ΣS_(j)C_(j) and wherein the summation includes all thecolorants in each of the preliminary colorant combinations,

ΔC is the vector of concentration adjustments to C matrix of Equation12, and

Δt is the vector of tristimulus color differences between the targetcoating and the approximate match of concentration C given by Equation12.

The concentration adjustments from Equation 13 are applied to theconcentrations from Equation 12. These new concentrations are thensubstituted in Equation 9 to calculate new (K/S)_(mix) at eachwavelength, which in turn are used in Equation 8 to generate a newspectral curve. Color differences between the new spectral curve andthat of the target are calculated by using the aforedescribed EquationA. This process is repeated iteratively until the color differences areacceptably small for the specified end use.

The color matching criteria described above allows a computer program tochoose various preliminary colorant combinations and get the theoreticalconcentration for each colorant in each of those preliminary colorantcombinations. It is possible that the solution of Equations 12 and 13could provide negative concentrations. For example, if a blue pigmentwas included in attempting to match the yellow-shade red example shownabove, the only way it could be matched would be to use a negativeamount of blue (complement of yellow), which would be physicallyimpossible and thus the color matching criteria can be configured toautomatically eliminate such combinations. The theoreticalconcentrations of colorants in the preliminary colorant combinations inFormulas 1, 2 and 3 as determined though the color matching criteriaexpressed in Equations 12 and 13 are shown in Table 6 below:

TABLE 6 Colorant Concentrations Colorants Formula 1 Formula 2 Formula 3White 0.52 0.34 0.34 Black 1.61 0.16 0.42 Red Oxide 2.75 1.38 Red1 7.23Yellow 1.79 1.12 0.9 Red2 4.18 Red3 1.47

Metallic colors can be also matched through similar processes. Theabsorption and scattering coefficients for colorants are then generallydetermined relative to aluminum flake dispersion instead of white. The Kand S values for each pigment must be determined separately at each ofthe angles of measurement. A problem can arise at low aspecular angles(e.g., 15 or 25 degrees) where reflectances (R) may exceed 1.0 for verylight colors, making Equation 8 ambiguous because of the squared term,i.e., the same value of K/S can be obtained for two different values ofR. Values of R greater than 1.0 are possible because the reflectance(referred to as reflectance factor in ASTM E-284) is determined as thereflectance of the color sample at a particular angle of measurement ascompared to that of the perfect diffuser at that same measurementcondition. Pressed barium sulfate is a good approximation of a perfectdiffuser. At these near-specular angles, bright aluminum flakes canexceed the lightness of the perfect diffuser measured at that sameangle. One of the ways of determining concentrations in the preliminarycolorant combination that includes metallic flakes is provided in claim8 and also at Column 9, line 55-column 10, line 61 and column 18, line9-column 28, line 5 in the U.S. Pat. No. 5,231,472. Yet another modelfor gonioapparent colors is discussed in Kettler, W. H., Kolb, M.,“Numerical evaluation of optical single-scattering properties ofreflective pigments using multiple-scattering inverse transportmethods”, Die Farbe, Vol. 43, pg. 167 (1997) and Kettler, W. H., Kolb,M., “Inverse multiple scattering calculations for plane-parallel turbidmedia: application to color recipe formulation”, in Proceedings of theInternational Workshop, Electromagnetic Light Scattering, Theory andApplication, Lomonosov State University, Moscow, Edited by Y. Eremin andTh. Wriedt (1997). All of the foregoing references are incorporatedherein by reference.

Since, the matched compositions need to be balanced to achieve thedesired film properties, step (v) of the method of the present inventionincludes balancing the preliminary colorant combinations to allow forthe presence of non-colorant components, such as binder polymers orsolvents, in the matched coating composition to generate one or moreviable combinations optimized in accordance with mixing and regulatorycriteria developed for the specified end-use.

It is well understood in the coating art to balance the variouscomponents in a coating compositions based on the specific end use thatis desired. For example, the durability requirement of a coating in aninterior application, such as wall coatings applied over interior wallsof a house would be less important than the durability requirements ofoutdoor coatings applied to exterior walls of a house that get exposedto UV radiation from the sun light. Similarly, the coating propertiesrequirements for coating compositions used in disparate geographiclocations, such as those used in cold and wet climates, such as inCanada would be far different than the those used in hot and aridclimates, such as in Saharan desert. By way another example, theadhesion properties of coatings used in automotive applications would bedifferent than those coatings used on coating home appliances. Thoseskilled in the coating arts empirically develop their own mixing andregulatory criteria tailored for a specified end-use.

Thus, the presence of other non-colorant components is necessary toprovide the resulting coating composition with application propertiesand good coating properties, such as adhesion, gloss, and durability,when a layer of the coating composition applied over a substrate surfacecures into a coating. A non-colorant component, such as a solvent, istypically included in a coating composition to improve its applicationproperties that result in an even flow out after spraying, without an“orange peel” surface or sagging on a vertical surface.

Thus, too little film build can adversely affect the hiding obtained bythe coating and too much film build can result in sagging of the paintlayer as it dries into a coating. Car refinishers also prefer automotivepaints to cover the substrate in two coats since a single coat hidingcan result in a splotchy appearance. However, application of more thantwo coats increases the labor cost and paint cost required to repair thecar and is thus undesirable.

Other non-colorant components, such as binder polymers, are alsoincluded in the coating composition to improve, for example, theadhesion of the resulting coating to the underlying substrate. It isalso desirable to balance the non-colorant components, such as solvent,in the coating composition, to meet regulatory requirements such as, forexample, lowering the volatile organic content (VOC) of the coatingcomposition. Other non-colorant components used include additives, suchas UV screeners, hindered amine light stabilizers for improvingdurability, rheology control agents, flow agents, adhesion promoters,catalysts and anti-crater agents. Yet another example of a commonrequirement would be to control the solids of a coating composition.Coating solids level affects such properties as the rate of film build,rheology, VOC and cost of the coating composition. Typically, solids arerestricted to a narrower range, such as for example, coating solids fora high solids refinish coating compositions being at about 60%±1%.

Percent solids for the coating can be expressed by the followingformula:100*(ΣSW_(i)/ΣTW_(i))  (14)where the solids weight of each component SW₁ to SW_(i) in a coatingcomposition is summed up and then divided by the sum of the total weightof each individual component TW₁ to TW_(i), i.e., (includes a solid partand a liquid part, if used, of each individual component).

One skilled in the art would recognize that the solids weight (SW), asused in the current context, includes all components that form part ofthe resultant coating, even though in the coating composition they mayhave been in a liquid form. For example, crosslinkers, which are often,low in the molecular weight and can be present, as liquid in the coatingcomposition then become part of the coating structure when thecrosslinkers in the coating composition crosslink after application.Thus, the desired solids requirement (the amount solvent used and/oramount and type of binder polymers used), such as those for low solidsor high solids matched coating composition, can be obtained by using theaforementioned Equation 14.

It may be necessary for the matched coating composition to meetenvironmental regulatory requirements, such as limiting the VOC of thematch coating composition as promulgated from time to time by thevarious government agencies, such as the Environmental Protection Agencyof the United States. One of the limits typically specified throughvarious statutes and regulations is to limit the weight of a solventincluded in a specified volume of coating composition. The VOC isnormally expressed as kilograms of solvent per liter of coatingcomposition, or in the United States it can be expressed as pounds ofsolvent per gallon of a coating composition. Such a limitation can varyin accordance with the intended use. The aforedescribed VOC limitationcan be expressed by the following formula:ΣS_(i)/V  (15)where the weight of the solvent in kilograms for each component S₁ toS_(i) is summed and divided by the volume of the final coatingcomposition expressed in liters. Thus, it is readily apparent that evenother requirements for the matched coating composition could beprogrammed by using suitably developed formulas to balance the colorformula based on the types and amounts non-colorant components requiredto meet the requirement for a specified end use.

Table 7 below shows the results of the foregoing balancing step used foroptimizing the preliminary colorant combinations into the viablecolorant combinations (Formulas* 1, 2 and 3) by including the amount ofthe balancing component needed to meet the mixing and regulatorycriteria for a specified end use.

TABLE 7 Colorant Concentrations Colorants Formula* 1 Formula* 2 Formula*3 White 0.52 0.34 0.34 Black 1.61 0.16 0.42 Red Oxide 2.75 1.38 Red17.23 Yellow 1.79 1.12 0.9 Red2 4.18 Red3 1.47 Balancing Component 86.192.81 96.86 Total 100 100 100

Step (vi) of the present method comprises selecting an optimal viablecombination from the viable colorant combinations (Formulas* 1, 2, and 3in Table 7 above) in accordance with an acceptability equation for thespecified end-use, the optimal viable combination having an optimalacceptability value for the specified end-use wherein the knowncolorants and non-colorant components when mixed in accordance with theoptimal. viable combination produce the matched coating composition thatwhen applied as a matched coating visually matches with the appearanceof the target coating.

The aforementioned acceptability equation for a specified end use isexpressed as:Acceptability value=ΣAcceptability factor_(i)*weight_(i)  (16)

Depending on the specified end use, a weight can be empiricallydeveloped for each of the following acceptability factors used incalculating the acceptability value. The summation of the acceptabilityfactors multiplied by the weight assigned to each such factor results inthe acceptability value of the matched composition in accordance withthe aforementioned Equation 16. The lower the acceptability value forthe specified end use, the more optimal would be viable combination.

Several of the following acceptability factors can be calculated foreach viable colorant combination:

1. Color difference: This factor relates to the degree of colordifference between the target coating and a matched coating obtainedfrom a coating composition formulated in accordance with each of theviable colorant combinations (Formulas* 1, 2 and 3). Several colordifference equations published in the literature can be used. TheInternational Committee on Illumination (CIE) in 1994 recommended acolor difference metric now referred to as the aforedescribed “CIE94Equations” or the “CMC Equations”. These equations provide amathematical estimate of the accuracy of color match that would beobserved by a normal observer under a given lighting condition,typically using the D65 illuminant, representing average daylight.

2. Metamerism: A match may appear acceptable under one illuminant butnot another or when viewed by different observers. Metamerism Indicescalculate color differences under two different illuminants (usually D65and A, which can be a common incandescent or fluorescent light). Thevector difference between these two color differences is calculated asan indicator of metamerism. The following equations can be used todetermine the metamerism:

The Tannenbaum Metamerism Index can be determined by the followingequations:G ₀=−0.4632X ₀+1.3677Y ₀+0.0955Z ₀  (17)B ₀=−0.4632X ₀+1.3677Y ₀+0.0955Z ₀  (18)R ₀=0.7584X ₀+0.3980Y ₀−0.1564Z ₀  (19)

Where X₀, Y₀, and Z₀ are the X, Y and Z of the illuminant.R=(0.7584X+0.3980Y−0.1564Z)*100/G ₀  (18)G=(−0.4632X+1.3677Y+0.0955Z)*100/G ₀  (19)B=(−0.1220X+0.3605Y+0.7615Z)*100/G ₀  (20)L=25G ^(1/3)−16  (21)a=a′−(Y/100)^(1/3) a ₀  (22)b=b′−(Y/100)^(1/3) b ₀  (23)wherea′=500[(R/100)^(1/3)−(G/100)^(1/3)]  (24)b′=200[(G/100)^(1/3)−(B/100)^(1/3)]  (25)

-   -   a₀, b₀ are calculated from these equations by using R₀,G₀,B₀ and        therefore Metamerism index MI is provided by:        MI=√{square root over ((ΔL _(C) −ΔL _(A))²+(Δa _(C) −Δa        _(A))²+(Δb _(C) −Δb _(A))²)}{square root over ((ΔL _(C) −ΔL        _(A))²+(Δa _(C) −Δa _(A))²+(Δb _(C) −Δb _(A))²)}{square root        over ((ΔL _(C) −ΔL _(A))²+(Δa _(C) −Δa _(A))²+(Δb _(C) −Δb        _(A))²)}  (26)

The lower the metamerism (MI), the better would be the color match undervarious lighting conditions.

3. Closeness of spectral curve match: When the same pigmentation andconcentrations are used in the target and matched coatings, theirspectral curves would be identical. This would be the ideal match interms of color accuracy. Thus an indicator of closeness of spectralcurve match is also a useful index; An example of this acceptabilityfactor sometimes referred to as the Reilly Metamerism Potential is shownbelow. Other measures of closeness of spectral curve match that are alsosuitable are provided by Nimeroff, I., and Yurow, J. A., in “Degree ofMetamerism”, J. Opt. Soc. Am., Volume 55, 185-190 (1965), which isincorporated herein by reference.

Reilly Metamerism Potential is obtained by the following equation:

$\begin{matrix}{{{Metamerism}\mspace{14mu}{Potential}} = \sqrt{{K_{L}^{2}\left( \frac{\Delta\; G}{G_{0}^{2/3}} \right)}^{2} + {K_{a}^{2}\left( {\frac{\Delta\; R}{R_{0}^{2/3}} - \frac{\Delta\; G}{G_{0}^{2/3}}} \right)}^{2} + {K_{b}^{2}\left( {\frac{\Delta\; G}{G_{0}^{2/3}} - \frac{\Delta\; B}{B_{0}^{2/3}}} \right)}^{2}}} & (27)\end{matrix}$whereΔR=Σ|A _(r)·ρ_(bλ)−ρ_(sλ)|· r _(λ),ΔG=Σ|A _(g)·ρ_(bλ)−ρ_(sλ)|· g _(λ), andΔB=Σ|A _(b)·ρ_(bλ)−ρ_(sλ)|· b _(λ);andA _(r) =R ₀ /R _(b) ,A _(g) =G ₀ /G _(b) ,A _(b) =B ₀ B _(b),R=X/X ₀ ,G=Y/Y ₀ ,B=Z/Z ₀;r ₈₀ = x _(λ) /X ₀, g _(λ) = y _(λ) /Y ₀, b _(λ) = z _(λ) /Z ₀;

x _(λ), y _(λ), z _(λ) being the tristimulus observer weightingfunctions; and

X, Y, and Z being the tristimulus values of target or matched coating.

In the foregoing, the subscript “0” refers to the corresponding X, Y,and Z for the illuminant.

K_(L) 25.00, K_(a) 107.72 and K_(b) is 43.09, which are the CIELABcoordinate scaling factors.

ρ_(λ)=spectral reflectance at wavelength λ,

subscript s refers to the target coating and b refers to the matchedcoating, and

R (X/X₀), G (Y/Y₀), B (Z/Z₀) are preferably computed for the standardobserver and the equal energy spectrum.

4. Durability: Depending on its end-use, this acceptability factor of acoating composition can be an important factor. Some colorants are moredurable than others. Each colorant can be assigned a “durabilityindicator” based on empirical durability tests, such as Florida exposurestudies. The sum of the concentration-weighted indicators of eachcolorant in the viable colorant combination can be used as a durabilityindex of that formula.

5. Cost: Depending on its end-use, this acceptability factor may or maynot be an important factor. For example, in automotive refinishapplications, durability and accuracy of color match far outweigh thecost of the coating composition. Moreover, the cost of the coatingcomposition is less significant when compared to the labor costsincurred in repairing an autobody. Since inaccurate color matchincreases the labor cost in completing the autobody repair and poordurability of auto paint can result in warrantee complaints, thesefactor far outweigh the paint costs. In view of the foregoing, the costthe resultant coating compositions in automotive refinish applicationwill be assigned substantially less weight as compared to the otherfactors, such as durability and accuracy of color match. By contrast,with interior wall paints however, the paint is generally not exposed tostrong sunlight or corrosive atmospheres, so the durability factor isless important. Accuracy of color match is also not of great concern aslong as the color consistency is maintained from batch-to-batch. Costhowever is an important factor for wall paints. Costs of ingredients andingredient densities can be stored in the database of the computer usedby the characterizing device of the present invention to compute thecost per unit volume of paint from the formula.

For example, an automotive customer usually requires a good match,regardless of cost, while durability is also important. Hence colordifference may be assigned a weight of 30, closeness of curve match aweight of 30, metamerism a weight of 25, durability a weight of 15 andcost a weight equal to zero.

The foregoing provides acceptability values of 46.5 for Formula* 1,193.6 for Formula* 2, 257.5 for Formula 3; clearly indicating thatFormula* 1 should be used in case of automotive refinish application.

Table 8 shows possible weighting factors for cases where low cost isimportant (resulting in the choice of Formula* 3; and where highdurability is most important, resulting in the choice of Formula* 2.These weights may be tailored to a particular customer or particular enduse for the coating composition.

Note that for gonioapparent colors the color differences, metamerism,and closeness of spectral match should be calculated at multiple angles(preferably 3 to 5) and then combined. Angles can be weighted inaccordance with the user or customer preference, if known.

TABLE 8 Calculation of Durability and Cost Indices Formula* 1 Formula* 2Formula* 3 D.I. C. A.F. C A.F. C A.F. White 0 0.52 0 0.34 0 0.34 0 Black0 1.61 0 0.16 0 0.42 0 Red Oxide 0 2.75 0 1.38 0 0 Red1 2 7.23 14.46 0 0Yellow 1 1.79 1.79 1.12 1.12 0.9 0.9 Red2 1 0 4.18 4.18 0 Red3 2 0 01.47 2.94 B.C. 86.1 92.81 96.86 Total 100 16.25 100 5.3 100 3.84 Total,13.9 7.18 3.13 (colorants weights only) Durability 1.17 0.74 1.23 IndexCost per $3.61 $2.90 $2.42 0.2 liters Notes: 1. D.I. means durabilityindicator. 2. C. means Concentration. 3. A.F. means acceptabilityfactor. 4. B.C. means balancing components, such as solvent and binderpolymers. 5. The concentration of each ingredient is multiplied by itsdurability indicator to arrive at the acceptability factor for thatingredient. 6. These acceptability factors are totaled and then dividedby the total weight of the colorants to provide the durability index ofthat formula. 7. The cost in US dollars per 0.2 liters is used so as tokeep its magnitude in line with other factors.

TABLE 9 Weights for Higher Formula* Formula* Formula* Closer Lower dura-Factors 1 2 3 match cost bility CIE94 0.08 1.13 1.89 30 10 10 ΔE Reilly0.67 4.32 4.82 30 0 0 Poten- tial T.M.I. 0.26 0.76 1.51 25 5 10 Dura-1.17 0.74 1.23 15 5 80 bility Cost/ 3.61 2.90 2.42 0 80 0 .02 lit Totals100 100 100 T.M.I. means Tannenbaum metamerism index

TABLE 10 Calculated Acceptability Values Degree of match between targetand Cost of coating matched coatings from composition from Durability ofmatched Formulas Formulas coating from Formulas Factors Rx 1 Rx 2 Rx 3Rx 1 Rx 2 Rx 3 Rx 1 Rx 2 Rx 3 CIE94 ΔE 2.4 33.9 56.7 0.8 11.3 18.9 0.811.3 18.9 Reilly Potential 20.1 129.6 144.6 0 0 0 0 0 0 T.M.I. 6.5 1937.75 1.3 3.8 7.55 2.6 7.6 15.1 Durability 17.5 11.1 18.4 5.8 3.7 6.193.5 59.1 98.1 Cost/.02 liter 0.0 0.0 0.0 288.7 232.1 194.0 0.0 0.0 0.0Totals 46.5 193.6 257.5 296.7 250.9 226.5 96.9 78.0 132.1 Rx meansFormula*.

Example of calculating the acceptability value:

Formula* 1 was found to have a CIE94 ΔE=0.08, as reported in Table 9.The weight assigned for the “best match” formula was 30. Hence the CIE94ΔE acceptability was 0.08×30=2.4 (reported in Table 10). Similarly theReilly Potential acceptability was 0.67×30=20.1. PMT Index acceptabilitywas 0.26×25=6.5. Durability acceptability was 1.17×15=17.5 (reported inTable 10). Cost/0.02 liter acceptability was 3.61×0=0 (reported in Table10). The summation of weight times the acceptability factor total up tothe acceptability value of Formula* 1 at 46.5.

As reported in Table 10, Formulas* 2 and 3 can be similarly reported.Since the acceptability value for color match for Formula I is thelowest, it would be chosen as the best formula when the criterion foracceptability is color match rather than cost or durability.

Similar calculations show that Formula* 3 as being the best when cost ismore important and Formula* 2 as being the best when durability is moreimportant.

The method of the present invention further comprises displaying on ascreen of a monitor of the device the optimal viable combination, whichhas the best acceptability value, i.e., the lowest acceptability valuefor the specified end use.

The method of the present invention also comprises mixing thecomponents, such as colorants, solvents, binder polymers, and additiveslisted in the optimal viable combination using conventional mixers toproduce the matched coating composition.

The method of the present invention also comprises applying the matchedcoating composition over a substrate, such as automotive body, byconventional application methods, such as spraying, roller coating, ordip coating, to produce the matched coating that visually matches withthe appearance of the target coating.

The matched coating composition produced or obtained in accordance withthe method of the present invention can be an OEM automotive paint,refinish automotive paint, architectural paint, industrial coatingcomposition, powder coating composition, printing ink, ink jet ink, nailpolish, food colorant, eye shadow, or hair dye.

Another embodiment of the method of present invention comprisesproducing a matched resin, such as those processed in injection molding,blow molding, rotational molding, thermoforming or extruding into aspecified end-use, such as dashboard, interior door panels or bumperguard of an automobile; or consumer products. The process can providethe formulator with an optimal viable combination for said specifiedend-use, such as that components in the optimal viable combination whenmixed produce a matched resin that when formed as a matched substratevisually matches with the appearance of a target substrate, such asautomobile upholstery or autobody.

The foregoing method can further comprise:

(a) mixing the components in the optimal viable combination with a resinto produce the matched resin; and

(b) processing the matched resin into the matched substrate.

The foregoing mixing step can be conventionally accomplished by meltingand extruding the components through a conventional extruder into thematched resin and then converting it in a powder or pelletized form.

The present Invention is also directed to a color characterizing device1 shown in FIG. 1 for producing a matched coating composition for aspecified end-use. Device 1 comprises:

(i) a spectrophotometer 2 of device 1, such as a conventionalmulti-angle spectrophotometer or sphere geometry spectrophotometer,having a base for positioning spectrophotometer 2 over a target portionof a target coating;

(ii) means for calculating target color (L,a,b or L,C,h) values of thetarget portion;

(iii) a computer usable storage medium 4 located in a computer 6 ofdevice 1 having computer readable program code means residing therein,the computer readable program code means comprising:

(a) means for configuring computer readable program code devices tocause computer 6 to select one or more preliminary colorant combinationsfrom a stored list of known colorants in accordance with a combinatorialselection criteria to match with the target color space values;

(b) means for configuring computer readable program code devices tocause computer 6 to determine concentration of each the known colorantin each of the preliminary colorant combinations in accordance withcolor matching criteria wherein the concentration of each the knowncolorant is optimized for optimal match of color values of each of thepreliminary colorant combinations with the target color values;

(d) means for configuring computer readable program code devices tocause computer 6 to balance the preliminary colorant combinations toallow for the presence of non-colorant components in the matched coatingcomposition to generate one or more viable combinations optimized inaccordance with mixing and regulatory criteria developed for thespecified end-use; and

(e) means for configuring computer readable program code devices tocause computer 6 to select an optimal viable combination from the viablecombinations in accordance with an acceptabiiity equation for thespecified end-use, the optimal viable combination having an optimalacceptability value for the specified end-use wherein the knowncolorants and non-colorant components when mixed in accordance with theoptimal viable combination produce the matched coating composition thatwhen applied as a matched coating visually matches with the appearanceof the target coating.

Device 1 further comprises means for configuring computer readableprogram code devices to cause computer 6 to display on a screen of amonitor 8 of device 1 the optimal viable combination.

Device 1 can further comprise:

(a) means for configuring computer readable program code devices tocause computer 6 to generate a signal in accordance with the optimalviable combination to dispense the components for making a desiredamount of the matched coating composition;

(b) a dispenser 10 for dispensing the components in a container 12,dispenser 10 being in communication with computer 6:

(c) means for configuring computer readable program code devices tocause computer 6 to generate a signal upon completion of making thedesired amount of the matched coating composition; and

(d) means for configuring computer readable program code devices tocause computer 6 to generate a signal to dispenser 10 to stop dispensingof the components.

Device 1 can further comprise a mixer, not shown in FIG. 1, for mixingthe components dispensed in container 12.

Device 1 of the present invention is a preferably transportable deviceto permit ready positioning of spectrophotometer 2 of device 1 onsubstrate of various shapes, such as automotive body.

Generally, the computer readable program code means of the presentinvention can be stored on a conventional portable computer usablestorage medium, such as a CD-Rom and the computer readable program codecan be programmed by using conventional programming software, such asC++Builder, Version 5 or Delphi, Version 6, both supplied by BorlandCorporation located in Scotts Valley, Calif.

Computer 6 suitable for use in the present invention can be anyconventional computer/processor such as those supplied by Dell ComputerCorporation. Round Rock, Tex. or IBM Corporation, Armonk, N.Y. that canbe configured to execute conventional computer program codes. Forexample, Model No. Dimension™4100 supplied by Dell Computer Corporationutilizing Windows® XP operating system supplied by Microsoft Corporationlocated in Redmond, Wash. can be utilized.

The present method is equally well suited for using a computer set upwherein computer 6 of device 1 is in communication with a host computer,not shown. It would be understood that the communication between thehost computer and computer 6 of device 1 can be through a modem or via awebsite. Moreover, the database of the stored list of known colorantscan reside either on a storage device of computer 6 of device 1 or on astorage device of the host computer. It should be understood thatcomputer 6 of device 1 and the host computer can be located anywhere,such as for example computer 6 of device 1 can be located in onecountry, such as the United States, or another state and the hostcomputer can be located in another country, such as Canada, or anotherstate. Alternatively, the host computer can be located In one county,such as United States, or another state and computer 6 of device 1 canbe located in another country, such as Canada, or another state. Itshould be further understood that the host computer could be incommunication with plurality of computers 6 of devices 1 being used.

1. A method for producing a matched coating composition for a specifiedend-use, said method comprising: (i) measuring reflectances of a targetportion of a target coating at a set of preset wavelengths with aspectrophotometer of a coating characterizing device to plot a targetspectral curve of said target portion, wherein said target coating is onan undamaged portion of an auto body, plastic substrate, marinesubstrate, and aluminum substrate; (ii) calculating target color (L,a,bor L,C,h) values of said target portion from said target spectral curveof said target portion; (iii) selecting one or more preliminary colorantcombinations from a stored list of known colorants in accordance with acombinatorial selection criteria to match with said target color values,wherein said stored list of known colorants comprises pigments,dispersions, tints, dyes, metallic flakes or a combination thereof, andwherein said combinatorial selection criteria comprise avoiding shadingwith complementary colorants and preferring colorant combinations with afewer number of pigments than a greater number of pigments; (iv)determining concentration of each said known colorant in each of saidpreliminary colorant combinations in accordance with color matchingcriteria wherein said concentration of each said known colorant isoptimized for optimal match of color values of each of said preliminarycolorant combinations with said target color values; (v) balancing saidpreliminary colorant combinations to allow for presence of non-colorantcomponents in said matched coating composition to generate one or moreviable combinations optimized in accordance with mixing and regulatorycriteria developed for said specified end-use; (vi) selecting an optimalviable combination from said viable combinations in accordance with anacceptability equation for said specified end-use, said optimal viablecombination having an optimal acceptability value for said specifiedend-use wherein said known colorants and non-colorant components whenmixed in accordance with said optimal viable combination produce saidmatched coating composition that when applied as a matched coatingvisually matches with appearance of said target coating, wherein saidacceptability equation is a summation of acceptability factorsmultiplied by a weight assigned to each said acceptability factor,wherein said acceptability factors comprise color difference,metamerism, closeness of spectral curve match, durability or cost; and(vii) displaying on a screen of a monitor of said device said optimalviable combination.
 2. The method of claim 1 further comprising mixingsaid components of said optimal viable combination to produce saidmatched coating composition.
 3. The method of claim 1 wherein saidmatched coating composition is an OEM automotive paint, refinishautomotive paint architectural paint, industrial coating composition,powder coating composition, printing ink, ink jet ink, nail polish, foodcolorant, eye shadow, or hair dye.
 4. The method of claim 1 wherein eachof said preliminary colorant combinations comprises one to seven saidknown colorants.
 5. The method of claim 1 wherein said step (ii)comprises: (a) directing a beam of light of a known intensity towardssaid target portion; and (b) sequentially measuring at at least oneaspecular angle said reflectances of said target portion at said set ofpreset wavelengths.
 6. The method of claim 1 wherein said step (ii)comprises: (a) sequentially directing one or more beams of light of aknown intensity at at least one incident angle towards said targetportion; and (b) sequentially measuring at an aspecular angle saidreflectances of said target portion at said set of preset wavelengths.7. The method of claim 1 further comprising applying said matchedcoating composition over a substrate to produce said coating thatvisually matches the appearance of said target coating.
 8. The method ofclaim 7 wherein said substrate is an automotive body.
 9. A matchedcoating composition produced by the method of claim
 1. 10. A colorcharacterizing device for producing a matched coating composition for aspecified end-use, said device comprising: (i) a spectrophotometer ofsaid device having a base for positioning said spectrophotometer over atarget portion of a target coating, wherein said target coating is on anundamaged portion of an auto body, plastic substrate, marine substrate,and aluminum substrate; (ii) means for calculating target color (L,a,bor L,C,h) values of said target portion; (iii) a computer usable storagemedium located in a computer of said device having computer readableprogram code means residing therein, said computer readable program codemeans comprising: (a) means for configuring computer readable programcode devices to cause said computer to select one or more preliminarycolorant combinations from a stored list of known colorants inaccordance with a combinatorial selection criteria to match with saidtarget color values, wherein said stored list of known colorantscomprises pigments, dispersions, tints, dyes, metallic flakes or acombination thereof, and wherein said combinatorial selection criteriacomprise avoiding shading with complementary colorants and preferringcolorant combinations with a fewer number of pigments than a greaternumber of pigments; (b) means for configuring computer readable programcode devices to cause said computer to determine concentration of eachsaid known colorant in each of said preliminary colorant combinations inaccordance with color matching criteria wherein said concentration ofeach said known colorant is optimized for optimal match of color valuesof each of said preliminary colorant combinations with said target colorvalues; (c) means for configuring computer readable program code devicesto cause said computer to balance said preliminary colorant combinationsto allow for presence of non-colorant components in said matched coatingcomposition to generate one or more viable combinations optimized inaccordance with mixing and regulatory criteria developed for saidspecified end-use; and (d) means for configuring computer readableprogram code devices to cause said computer to select an optimal viablecombination from said viable combinations In accordance with anacceptability equation for said specified end-use, said optimal viablecombination having an optimal acceptability value for said specifiedend-use wherein said known colorants and non-colorant components whenmixed in accordance with said optimal viable combination produce saidmatched coating composition that when applied as a matched coatingvisually matches with appearance of said target coating, wherein saidacceptability equation is a summation of acceptability factorsmultiplied by a weight assigned to each said acceptability factor,wherein said acceptability factors comprise color difference,metamerism, closeness of spectral curve match, durability or cost. 11.The device of claim 10 further comprising means for configuring computerreadable program code devices to cause said computer to display on ascreen of a monitor of said device said optimal viable combination. 12.The device of claim 10 wherein said device is a transportable device.13. The device of claim 10 wherein said spectrophotometer is amultiangle spectrophotometer.
 14. The device of claim 10 wherein saidspectrophotometer is a sphere geometry spectrophotometer.
 15. The deviceof claim 10 further comprising: (a) means for configuring computerreadable program code devices to cause said computer to generate asignal in accordance with said optimal viable combination to dispensesaid components for making a desired amount of said matched coatingcomposition; (b) a dispenser for dispensing said components in acontainer, said dispenser being in communication with said computer; (c)means for configuring computer readable program code devices to causesaid computer to generate a signal upon completion of making saiddesired amount of said matched coating composition; and (d) means forconfiguring computer readable program code devices to cause saidcomputer to generate a signal to said dispenser to stop dispensing ofsaid components.
 16. The device of claim 15 further comprising a mixerfor mixing said components dispensed in said container.
 17. The deviceof claim 10 or 15 wherein said computer is in communication with a hostcomputer.
 18. A method for producing a matched resin for a specifiedend-use, said method comprising: (i) measuring reflectances of a targetportion of a target substrate at a set of preset wavelengths with aspectrophotometer of a coating characterizing device to plot a targetspectral curve of said target portion, wherein said target portion is onan undamaged portion of said target substrate comprising an auto body,plastic substrate or a marine substrate; (ii) calculating target color(L,a,b or L,C,h) values of said target portion from said target spectralcurve of said target portion; (iii) selecting one or more preliminarycolorant combinations from a stored list of known colorants inaccordance with a combinatorial selection criteria to match with saidtarget color values, wherein said stored list of known colorantscomprises pigments, dispersions, tints, dyes, metallic flakes or acombination thereof, and wherein under said combinatorial selectioncriteria compriser avoiding shading with complementary colorants andpreferring colorant combinations with a fewer number of pigments than agreater number of pigments; (iv) determining concentrations of each saidknown colorant in each of said preliminary colorant combinations inaccordance with color matching criteria to generate one or moreintermediate colorant combinations of said known colorants wherein eachof said intermediate colorant combinations is optimized for optimalcolor match with said target color values; (v) balancing saidintermediate colorant combinations to allow for presence of non-colorantcomponents in said matched coating composition to generate one or moreviable combinations of said known colorants, wherein each of said viablecombinations is optimized in accordance with mixing and regulatorypractices developed for said specified end-use; (vi) selecting anoptimal viable combination from said viable combinations in accordancewith an acceptability equation for said specified end-use, said optimalviable combination having an optimal acceptability value for saidspecified end-use wherein components in said optimal viable combinationwhen mixed produce said matched resin that when formed as a matchedsubstrate visually matches appearance of said target substrate, whereinsaid acceptability equation is a summation of acceptability factorsmultiplied by weight assigned to each said acceptability factor, whereinsaid acceptability factors comprise color difference, metamerism,closeness of spectral curve match, durability or cost; and (vii)displaying on a screen of a monitor of said device said optimal viablecombination.
 19. The method of claim 18 wherein said matched substrateis a dashboard or interior door panels of an automobile and said targetsubstrate is automobile upholstery.
 20. The method of claim 18 whereinsaid matched substrate is an automobile bumper guard and said targetsubstrate is auto body.
 21. The method of claim 18 further comprising:(a) mixing said components in said optimal viable combination with aresin to produce said matched resin; and (b) processing said matchedresin into said matched substrate.
 22. The method of claim 21 whereinsaid processing step comprises injection molding, blow molding,rotational molding, thermoforming or extruding of said matched resin.23. A matched resin produced by the method of claim
 18. 24. A portablecomputer usable storage medium having computer readable program codemeans stored therein for producing a matched coating composition for aspecified end-use, said computer readable program code means comprising:(a) means for configuring computer readable program code devices tocause a computer to select one or more preliminary colorant combinationsfrom a stored list of known colorants in accordance with a combinatorialselection criteria to match with target color values of a target portionon an undamaged portion of a target substrate comprising an auto body,plastic substrate, or a marine substrate, wherein said stored list ofknown colorants comprises pigments, dispersions, tints, dyes, metallicRakes or a combination thereof and wherein said combinatorial selectioncriteria comprise avoiding shading with complementary colorants andpreferring colorant combinations with a fewer number of pigments than agreater number of pigments; (b) means for configuring computer readableprogram code devices to cause said computer to determine concentrationof each said known colorant in each of said preliminary colorantcombinations in accordance with color matching criteria wherein saidconcentration of each said known colorant is optimized for optimal matchof color values of each of said preliminary colorant combinations withsaid target color values; (c) means for configuring computer readableprogram code devices to cause said computer to balance said preliminarycolorant combinations to allow for presence of non-colorant componentsin said matched coating composition to generate one or more viablecombinations optimized in accordance with mixing and regulatory criteriadeveloped for said specified end-use; and (d) means for configuringcomputer readable program code devices to cause said computer to selectan optimal viable combination from said viable combinations inaccordance with an acceptability equation for said specified end-use,said optimal viable combination having an optimal acceptability valuefor said specified end-use wherein said known colorants and non-colorantcomponents when mixed in accordance with said optimal viable combinationproduce said matched coating composition that when applied as a matchedcoating visually matches with the appearance of a target coating,wherein said acceptability equation is a summation of acceptabilityfactors multiplied by a weight assigned to each said acceptabilityfactor, wherein said acceptability factors comprise color difference,metamerism, closeness of spectral curve match, durability or cost. 25.The portable computer usable storage medium of claim 24 furthercomprising means for configuring computer readable program code devicesto cause said computer to display on a screen of a monitor said optimalviable combination.
 26. The portable computer usable storage medium ofclaim 24 further comprising: (a) means for configuring computer readableprogram code devices to cause said computer to generate a signal inaccordance with said optimal viable combination to dispense said knowncolorants and said non-colorant components for making a desired amountof said matched coating composition; (b) a dispenser for dispensing saidknown colorants and said non-colorant components in a container, saiddispenser being in communication with said computer; (c) means forconfiguring computer readable program code devices to cause saidcomputer to generate a signal upon completion of making said desiredamount of said matched coating composition; and (d) means forconfiguring computer readable program code devices to cause saidcomputer to generate a signal to said dispenser to stop dispensing ofsaid known colorants and said non-colorant component.
 27. The portablecomputer usable storage medium of claim 24 wherein said medium isCD-Rom.